Mathematics and Physics Seminar Series

AnnouncingAnnouncing

A Seminar Presentation

on Thursday

November 16, 2017

at 3:00 pm in

North Hall 102

at The University of New Haven

Characterizing gaps of numerical

semigroups

— Dr. Caleb Shor

Associate Professor

Department of Mathematics

Western New England University

Abstract: For G a set of positive integers with gcd(G) = 1, a numer-

ical semigroup S is the set of all non-negative linear combinations of

elements of G. One can show that there are ﬁnitely many positive in-

tegers, called gaps, that are not in S. As we will see, questions about

gaps have been posed in numerous contexts, including coins, stamps,

basketball, and chicken nuggets.

In this talk, we will explore a few problems related to numerical

semigroups and their gaps, including computation of the largest gap

(called the “Frobenius problem”), and the cardinality and sum of the

set of gaps. Additionally, we will see connections to the Bernoulli

numbers along with some current research questions.

Fur ther Information

For further information, please contact Dr. Yasanthi Kottegoda at the Department of Math-

ematics and Physics, Ofﬁce: Maxcy 315, 203-932-1206, YKottegoda@newhaven.edu.